I think it’s 1.75 sorry if this is wrong
Answer:
40 girls
Step-by-step explanation:
if you multiply 5 times 10, then you have to multiply the other side by 10 too. So 5 times 10 equals 50, and 4 times 10 equals 40.
40+50+=90.
Answer:
It's C) 53
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
Since the triangle is right use the tangent ratio to find x
tan64° =
=
Multiply both sides by 11
x = 11 × tan64° = 22.55 → B
Using the critical point concept, it is found that a = -3 and b = 7.
<h3>What are the critical points of a function?</h3>
- The critical points of a function are the values of x for which:
![f^{\prime}(x) = 0](https://tex.z-dn.net/?f=f%5E%7B%5Cprime%7D%28x%29%20%3D%200)
In this problem, the function is:
![f(x) = x^3 + ax^2 + b](https://tex.z-dn.net/?f=f%28x%29%20%3D%20x%5E3%20%2B%20ax%5E2%20%2B%20b)
Hence, the derivative is:
![f^{\prime}(x) = 3x^2 + 2ax](https://tex.z-dn.net/?f=f%5E%7B%5Cprime%7D%28x%29%20%3D%203x%5E2%20%2B%202ax)
Then:
![f^{\prime}(x) = 0](https://tex.z-dn.net/?f=f%5E%7B%5Cprime%7D%28x%29%20%3D%200)
![3x^2 + 2ax = 0](https://tex.z-dn.net/?f=3x%5E2%20%2B%202ax%20%3D%200)
![x(3x + 2a) = 0](https://tex.z-dn.net/?f=x%283x%20%2B%202a%29%20%3D%200)
![x = 0](https://tex.z-dn.net/?f=x%20%3D%200)
![3x + 2a = 0](https://tex.z-dn.net/?f=3x%20%2B%202a%20%3D%200)
![3x = -2a](https://tex.z-dn.net/?f=3x%20%3D%20-2a)
![x = -\frac{2a}{3}](https://tex.z-dn.net/?f=x%20%3D%20-%5Cfrac%7B2a%7D%7B3%7D)
Since the critical point is at x = 2, we have that:
![-\frac{2a}{3} = 2](https://tex.z-dn.net/?f=-%5Cfrac%7B2a%7D%7B3%7D%20%3D%202)
![-2a = 6](https://tex.z-dn.net/?f=-2a%20%3D%206)
![2a = -6](https://tex.z-dn.net/?f=2a%20%3D%20-6)
![a = -3](https://tex.z-dn.net/?f=a%20%3D%20-3)
Then:
![f(x) = x^3 - 3x^2 + b](https://tex.z-dn.net/?f=f%28x%29%20%3D%20x%5E3%20-%203x%5E2%20%2B%20b)
Critical point at (2,3) means that when
, then:
![3 = 2^3 - 3(2)^2 + b](https://tex.z-dn.net/?f=3%20%3D%202%5E3%20-%203%282%29%5E2%20%2B%20b)
![8 - 12 + b = 3](https://tex.z-dn.net/?f=8%20-%2012%20%2B%20b%20%3D%203)
![b = 7](https://tex.z-dn.net/?f=b%20%3D%207)
You can learn more about the critical point concept at brainly.com/question/2256078